F. Domínguez-Adame

Experimental evidence of delocalized states in random dimer superlattices

We study the electronic properties of GaAs-AlGaAs superlattices with intentional correlated disorder by means of photoluminescence and vertical de resistance. The results are compared to those obtained in ordered and uncorrelated disordered superlattices. We report the first experimental evidence that spatial correlations inhibit localization of states in disordered low-dimensional systems, as our previous theoretical calculations suggested, in contrast to the earlier belief that all eigenstates are localized.

Bound states of the Klein-Gordon equation with vector and scalar Hulthén-type potentials

Abstract The existence of bound states for the s-wave Klein-Gordon equation for vector and scalar Hulthen-type potentials is shown, provided that the potential “size” is large enough. The solution can be explicitly written down in terms of hypergeometric functions. The effects of strong coupling on the bound states are discussed.

TRANSPORT THROUGH A QUANTUM WIRE WITH A SIDE QUANTUM-DOT ARRAY

A noninteracting quantum-dot array side coupled to a quantum wire is studied. Transport through the quantum wire is investigated by using a noninteracting Anderson tunneling Hamiltonian. The conductance at zero temperature develops an oscillating band with resonances and antiresonances due to constructive and destructive interference in the ballistic channel, respectively. Moreover, we have found an odd-even parity in the system, whose conductance vanishes for an odd number of quantum dots while it becomes 2e(2)/h for an even number. We established an explicit relation between this odd-even parity and the positions of the resonances and antiresonances of the conductivity with the spectrum of the isolated quantum-dot array.

Physical nature of critical wave functions in Fibonacci systems.

We report on a new class of critical states in the energy spectrum of general Fibonacci systems. By introducing a transfer matrix renormalization technique, we prove that the charge distribution of these states spreads over the whole system, showing transport properties characteristic of electronic extended states. Our analytical method is a first step to find out the link between the spatial structure of critical wave functions and their related transport properties. PACS numbers: 71.23.Ft, 61.44.‐n The notion of critical wave function (CWF) has evolved continuously since its introduction in the study of aperiodic systems [1], leading to a somewhat confusing situation. For instance, references to self-similar, chaotic, quasiperiodic, latticelike, or quasilocalized CWFs can be found in the literature depending on the different criteria adopted to characterize them [2‐6]. Generally speaking, CWFs exhibit a rather involved oscillatory behavior, displaying strong spatial fluctuations which show distinctive self-similar features in some instances. As a consequence, the notion of an envelope function, which has been most fruitful in the study of both extended and localized states, is mathematically ill-defined in the case of CWFs, and other approaches are required to properly describe them and to understand their structure. Most interestingly, the possible existence of extended states in several kinds of aperiodic systems, including both quasiperiodic [7 ‐ 10] and nonquasiperiodic ones [4,11], has been discussed in the last few years spurring the interest on the precise nature of CWFs and their role in the physics of aperiodic systems. From a rigorous mathematical point of view the nature of a state is uniquely determined by the measure of the spectrum to which it belongs. In this way, since it has been proven that Fibonacci lattices have purely singular continuous energy spectra [12], we must conclude that the associated electronic states cannot be, strictly speaking, extended in the Bloch’s sense. This result holds for other aperiodic lattices (Thue-Morse, period doubling) as well [13], and it may be a general property of the spectra of self-similar aperiodic systems [14]. On the other side, from a physical viewpoint, the states can be classified according to their transport properties which, in turn, are determined by the spatial distribution of the wave function amplitudes (charge distribution). Thus, conducting, crystalline systems are described by periodic Bloch states, whereas insulating systems are described by exponentially decaying wave functions corresponding to localized states. In this sense, since the amplitudes of CWFs in a Fibonacci lattice do not tend to zero at infinity but are bounded below throughout the system [15], one may expect their physical behavior to be more similar to that corresponding to extended states than to localized ones. In this Letter we are going to show analytically that a subset of the CWFs belonging to general Fibonacci systems are extended from a physical point of view. This result widens the notion of extended wave function to include electronic states which are not Bloch functions, and it is a relevant first step to clarify the precise manner in which the quasiperiodic order of Fibonacci systems influences their transport properties [16]. To this end we present, in the first place, a new renormalization approach opening, in a natural way, an algebraic formalism which allows us to give a detailed analytical account of the transport properties of CWFs for certain particular values of the energy. In the second place, we study the relationship between the spatial structure of CWFs and their transport properties, showing that self-similar wave functions are those exhibiting higher transmission coefficients in finite Fibonacci systems. The formalism we are going to introduce is based on the transfer matrix technique, where the solution of the Schrodinger equation is obtained by means of a product of 2 3 2 matrices. Real-space renormalization group approaches, based on decimation schemes, have proved themselves very successful in order to numerically obtain

Solvable Linear Potentials in the Dirac Equation

The Dirac equation for some linear potentials leading to Schrodinger-like oscillator equations for the upper and lower components of the Dirac spinor have been solved. Energy levels for the bound states appear in pairs, so that both particles and antiparticles may be bound with the same energy. For weak coupling, the spacing between levels is proportional to the coupling constant while in the strong limit those levels are depressed compared to the nonrelativistic ones.

Bloch-Like Oscillations in a One-Dimensional Lattice with Long-Range Correlated Disorder

We study the dynamics of an electron subjected to a uniform electric field within a tight-binding model with long-range-correlated diagonal disorder. The random distribution of site energies is assumed to have a power spectrum S(k) approximately 1/k(alpha) with alpha>0. de Moura and Lyra [Phys. Rev. Lett. 81, 3735 (1998)]] predicted that this model supports a phase of delocalized states at the band center, separated from localized states by two mobility edges, provided alpha>2. We find clear signatures of Bloch-like oscillations of an initial Gaussian wave packet between the two mobility edges and determine the bandwidth of extended states, in perfect agreement with the zero-field prediction.

Electron transport across a Gaussian superlattice

We study the electron transmission probability in semiconductor superlattices where the height of the barriers is modulated by a Gaussian profile. Such structures act as efficient energy band-pass filters and, contrary to previous designs, it is expected to present a lower number of unintentional defects and, consequently, better performance. The j–V characteristic presents negative differential resistance with peak-to-valley ratios much greater than in conventional semiconductor superlattices.

LINEAR OPTICAL PROPERTIES OF ONE-DIMENSIONAL FRENKEL EXCITON SYSTEMS WITH INTERSITE ENERGY CORRELATIONS

We analyze the effects of intersite energy correlations on the linear optical properties of one-dimensional disordered Frenkel exciton systems. The absorption linewidth and the factor of radiative rate enhancement are studied as a function of the correlation length of the disorder. Thr absorption line width monotonously approaches the seeding degree of disorder on increasing the correlation length. On the contrary, the factor of radiative rate enhancement shows a nonmonotonous trend, indicating a complicated scenario of the exciton localization in correlated systems. The concept of coherently bound molecules is exploited to explain the numerical results, showing good agreement with theory. Some recent experiments are discussed in the light of the present theory. [S0163-1829(99)07343-9].

Model for crystallization kinetics: Deviations from Kolmogorov–Johnson–Mehl–Avrami kinetics

We propose a simple and versatile model to understand the deviations from the well-known Kolmogorov–Johnson–Mehl–Avrami kinetics theory found in metal recrystallization and amorphous semiconductor crystallization. We analyze the kinetics of the transformation and the grain-size distribution of the product material, finding a good overall agreement between our model and available experimental data. The information so obtained could help to relate the mentioned experimental deviations due to preexisting anisotropy along some regions, to a certain degree of crystallinity of the amorphous phases during deposition, or more generally, to impurities or roughness of the substrate.

A ONE-DIMENSIONAL RELATIVISTIC SCREENED COULOMB POTENTIAL

Abstract We propose a screened Coulomb potential leading to an exactly solvable one-dimensional Dirac equation. Unlike the one-dimensional Coulomb potential, the screened potential can support truly bound states because the Klein paradox is absent, provided that the potential does not dive into the negative-energy continuum. The δ-function limit of the potential is considered in detail. In the conclusions we discuss possible applications of our results in different physical contexts.